Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can b...Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.展开更多
The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to phys...The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to physicists andmathematicians. Large number of bodies, huge masses, long distances and exponentially increasing number of equations of motion of the bodies have been themajor hurdles in solving this problem for large and complex galaxies. Adventof high performance computational machines have mitigated the problem to muchextent, but still for large number of bodies it consumes huge amount of resourcesand days for computation. Conventional algorithms have been able to reduce thecomputational complexity from O n2 ð Þ to O nlogn ð Þ by splitting the space into atree or mesh network, researchers are still looking for improvements. In thisresearch work we propose a novel solution to N-body problem inspired by metaheuristics algorithms. The proposed algorithm is simulated for various time periods of selected heavenly bodies and analyzed for speed and accuracy. Theresults are compared with that of conventional algorithms. The outcomes showabout 50% time saving with almost no loss in accuracy. The proposed approachbeing a metaheuristics optimization technique, attempts to find optimal solution tothe problem, searching the entire space in a unique and efficient manner in a verylimited amount of time.展开更多
A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with st...A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with state-of-the-art Hermite integrator. It is shown that this regularization keeps some features that allow overcoming KS-regularization in some particular cases.展开更多
Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal...Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal behavior of different physical parameters of active galactic nuclei (AGN) containing a super massive black hole (SMBH), an accretion disk, and a compact stellar cluster;2) calculation of the stellar capture rate to the central SMBH without accretion disk. The calculations show good perspectives for applications of the similarity method to optimize the evolution model calculations of large stellar systems and of AGN.展开更多
The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physica...The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.展开更多
A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the develo...A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the development of proper featurization method based on physicochemical nature of target proprieties can improve the predictive power of ML models with a smaller database.In this work,we show that two new featurization methods,volume occupation spatial matrix and heat contribution spatial matrix,can improve the accuracy in predicting energetic materials' crystal density(ρ_(crystal)) and solid phase enthalpy of formation(H_(f,solid)) using a database containing 451 energetic molecules.Their mean absolute errors are reduced from 0.048 g/cm~3 and 24.67 kcal/mol to 0.035 g/cm~3 and 9.66 kcal/mol,respectively.By leave-one-out-cross-validation,the newly developed ML models can be used to determine the performance of most kinds of energetic materials except cubanes.Our ML models are applied to predict ρ_(crystal) and H_(f,solid) of CHON-based molecules of the 150 million sized PubChem database,and screened out 56 candidates with competitive detonation performance and reasonable chemical structures.With further improvement in future,spatial matrices have the potential of becoming multifunctional ML simulation tools that could provide even better predictions in wider fields of materials science.展开更多
Two cases of the nested configurations in R3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case ...Two cases of the nested configurations in R3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (6) of masses.展开更多
Major mergers of galaxies are considered to be an efficient way to trigger Active Galactic Nuclei and are thought to be responsible for the phenomenon of quasars. This has however recently been challenged by observati...Major mergers of galaxies are considered to be an efficient way to trigger Active Galactic Nuclei and are thought to be responsible for the phenomenon of quasars. This has however recently been challenged by observations of a large number of low luminosity Active Galactic Nuclei at low redshift(z■1) without obvious major merger signatures. Minor mergers are frequently proposed to explain the existence of these Active Galactic Nuclei. In this paper, we perform nine high resolution hydrodynamical simulations of minor galaxy mergers, and investigate whether nuclear activities can be efficiently triggered by minor mergers, by setting various properties for the progenitor galaxies of those mergers. We find that minor galaxy mergers can activate the massive black hole in the primary galaxy with an Eddington ratio of f Edd > 0.01 and> 0.05(or a bolometric luminosity > 10^43 and > 10^44 erg s^-1) with a duration of 2.71 and 0.49 Gyr(or 2.69 and 0.19 Gyr), respectively. The nuclear activity of the primary galaxy strongly depends on the nucleus separation, such that the nucleus is more active as the two nuclei approach each other. Dual Active Galactic Nuclei systems can still possibly be formed by minor mergers of galaxies, though the time duration for dual Active Galactic Nuclei is only ~ 0.011 Gyr and ~ 0.017 Gyr with Eddington ratio of f Edd > 0.05 and bolometric luminosity > 10^44 erg s^-1. This time period is typically shorter than that of dual Active Galactic Nuclei induced by major galaxy mergers.展开更多
We introduce a new halo/subhalo finder,HIKER(a Halo fInder based on KERnel-shift algorithm),which takes advantage of a machine learning method–the mean-shift algorithm combined with the Plummer kernel function,to eff...We introduce a new halo/subhalo finder,HIKER(a Halo fInder based on KERnel-shift algorithm),which takes advantage of a machine learning method–the mean-shift algorithm combined with the Plummer kernel function,to effectively locate density peaks corresponding to halos/subhalos in density field.Based on these density peaks,dark matter halos are identified as spherical overdensity structures,and subhalos are bound substructures with boundaries at their tidal radius.By testing HIKER code with mock halos,we show that HIKER performs excellently in recovering input halo properties.In particular,HIKER has higher accuracy in locating halo/subhalo centres than most halo finders.With cosmological simulations,we further show that HIKER reproduces the abundance of dark matter halos and subhalos quite accurately,and the HIKER halo/subhalo mass functions and Vmax functions are in good agreement with two widely used halo finders,SUBFIND and AHF.展开更多
A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are e...A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ（r =√3/3ρ is the radius ratio of the sizes） and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ（ρ＋3）（3＋2ρ＋ρ^2）^-3/2＋ρ（-ρ＋3）（3-2ρ＋ρ^2）^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2（1＋ρ）（3＋2ρ＋ρ^2）^-3/2＋2（ρ-1）（3-2ρ＋ρ^2）^-3/2-4（2√2）^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval （0, 0.03871633950 ... ）, there exist three central configuration solutions（the initial configuration conditions who imply hamagraphic solutions） corresponding radius ratios are r1, r2, and r3, two of them in the interval （2.639300779… , ＋∞） and one is in the interval （0.7379549890…, 1.490942703… ）. when mass ratio τ is in the open interval （130.8164950… , ＋∞）, in the same way there have three corresponding radius ratios, two of them in the interval （0, 0.4211584789... ） and one is in the interval （0.7379549890…, 1.490942703…）. When mass ratio τ is in the open interval （0.03871633950…, 130.8164950…）, there has only one solution r in the interval （0.7379549890…, 1.490942703… ）.展开更多
The minimum energy and stable configurations in the spherical,equal mass full 4-body problem are investigated.This problem is defined as the dynamics of finite density spheres which interact gravitationally and throug...The minimum energy and stable configurations in the spherical,equal mass full 4-body problem are investigated.This problem is defined as the dynamics of finite density spheres which interact gravitationally and through surface contact forces.This is a variation of the gravitational n-body problem in which the bodies are not allowed to come arbitrarily close to each other(due to their finite density),enabling the existence of resting configurations in addition to orbital motion.Previous work on this problem has outlined an efficient and simple way in which the stability of configurations in this problem can be defined.This methodology is applied to the 4-body problem,where we find multiple resting equilibrium configurations and outline the stability of a number of these.The study of these configurations is important for understanding the mechanics and morphological properties of small rubble pile asteroids.These results can also be generalized to other configurations of bodies that interact via field potentials and surface contact forces.展开更多
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
基金The project supported by the National Natural Science Foundation of China
文摘Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.
基金This research study has been supported by National Center in Big Data and Cloud Computing,NED University of Engincering and Technology,Karachi,Pakistan.
文摘The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to physicists andmathematicians. Large number of bodies, huge masses, long distances and exponentially increasing number of equations of motion of the bodies have been themajor hurdles in solving this problem for large and complex galaxies. Adventof high performance computational machines have mitigated the problem to muchextent, but still for large number of bodies it consumes huge amount of resourcesand days for computation. Conventional algorithms have been able to reduce thecomputational complexity from O n2 ð Þ to O nlogn ð Þ by splitting the space into atree or mesh network, researchers are still looking for improvements. In thisresearch work we propose a novel solution to N-body problem inspired by metaheuristics algorithms. The proposed algorithm is simulated for various time periods of selected heavenly bodies and analyzed for speed and accuracy. Theresults are compared with that of conventional algorithms. The outcomes showabout 50% time saving with almost no loss in accuracy. The proposed approachbeing a metaheuristics optimization technique, attempts to find optimal solution tothe problem, searching the entire space in a unique and efficient manner in a verylimited amount of time.
文摘A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with state-of-the-art Hermite integrator. It is shown that this regularization keeps some features that allow overcoming KS-regularization in some particular cases.
文摘Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal behavior of different physical parameters of active galactic nuclei (AGN) containing a super massive black hole (SMBH), an accretion disk, and a compact stellar cluster;2) calculation of the stellar capture rate to the central SMBH without accretion disk. The calculations show good perspectives for applications of the similarity method to optimize the evolution model calculations of large stellar systems and of AGN.
文摘The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.
基金support from the Ministry of Education(MOE) Singapore Tier 1 (RG8/20)。
文摘A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the development of proper featurization method based on physicochemical nature of target proprieties can improve the predictive power of ML models with a smaller database.In this work,we show that two new featurization methods,volume occupation spatial matrix and heat contribution spatial matrix,can improve the accuracy in predicting energetic materials' crystal density(ρ_(crystal)) and solid phase enthalpy of formation(H_(f,solid)) using a database containing 451 energetic molecules.Their mean absolute errors are reduced from 0.048 g/cm~3 and 24.67 kcal/mol to 0.035 g/cm~3 and 9.66 kcal/mol,respectively.By leave-one-out-cross-validation,the newly developed ML models can be used to determine the performance of most kinds of energetic materials except cubanes.Our ML models are applied to predict ρ_(crystal) and H_(f,solid) of CHON-based molecules of the 150 million sized PubChem database,and screened out 56 candidates with competitive detonation performance and reasonable chemical structures.With further improvement in future,spatial matrices have the potential of becoming multifunctional ML simulation tools that could provide even better predictions in wider fields of materials science.
基金Supported by the NSF of China(10231010)Supported by the NSF of CQSXXY (20030104)
文摘Two cases of the nested configurations in R3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (6) of masses.
基金supported by the National Key Program for Science and Technology Research and Development (No. 2016YFA0400704)the National Natural Science Foundation of China (Nos. 11690024 and 11873056)the Strategic Priority Program of the Chinese Academy of Sciences (No. XDB 23040100)
文摘Major mergers of galaxies are considered to be an efficient way to trigger Active Galactic Nuclei and are thought to be responsible for the phenomenon of quasars. This has however recently been challenged by observations of a large number of low luminosity Active Galactic Nuclei at low redshift(z■1) without obvious major merger signatures. Minor mergers are frequently proposed to explain the existence of these Active Galactic Nuclei. In this paper, we perform nine high resolution hydrodynamical simulations of minor galaxy mergers, and investigate whether nuclear activities can be efficiently triggered by minor mergers, by setting various properties for the progenitor galaxies of those mergers. We find that minor galaxy mergers can activate the massive black hole in the primary galaxy with an Eddington ratio of f Edd > 0.01 and> 0.05(or a bolometric luminosity > 10^43 and > 10^44 erg s^-1) with a duration of 2.71 and 0.49 Gyr(or 2.69 and 0.19 Gyr), respectively. The nuclear activity of the primary galaxy strongly depends on the nucleus separation, such that the nucleus is more active as the two nuclei approach each other. Dual Active Galactic Nuclei systems can still possibly be formed by minor mergers of galaxies, though the time duration for dual Active Galactic Nuclei is only ~ 0.011 Gyr and ~ 0.017 Gyr with Eddington ratio of f Edd > 0.05 and bolometric luminosity > 10^44 erg s^-1. This time period is typically shorter than that of dual Active Galactic Nuclei induced by major galaxy mergers.
基金support from the National Key Program for Science and Technology Research and Development(2017YFB0203300)support from the National Natural Science Foundation of China(NSFC)(No.11425312)+4 种基金two Royal Society Newton Advanced Fellowshipsthe hospitality of the Institute for Computational Cosmology at Durham Universitysupported by NSFC(Grant Nos.11573033 and 11622325)the“Recruitment Program of Global Youth Experts”of Chinathe NAOC grant(Y434011V01)。
文摘We introduce a new halo/subhalo finder,HIKER(a Halo fInder based on KERnel-shift algorithm),which takes advantage of a machine learning method–the mean-shift algorithm combined with the Plummer kernel function,to effectively locate density peaks corresponding to halos/subhalos in density field.Based on these density peaks,dark matter halos are identified as spherical overdensity structures,and subhalos are bound substructures with boundaries at their tidal radius.By testing HIKER code with mock halos,we show that HIKER performs excellently in recovering input halo properties.In particular,HIKER has higher accuracy in locating halo/subhalo centres than most halo finders.With cosmological simulations,we further show that HIKER reproduces the abundance of dark matter halos and subhalos quite accurately,and the HIKER halo/subhalo mass functions and Vmax functions are in good agreement with two widely used halo finders,SUBFIND and AHF.
基金NSF of China(10231010)NSF of Chongqing EducationCommittee(071105)NSF of SXXYYB(070X)
文摘A new case configuration in R^3, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ（r =√3/3ρ is the radius ratio of the sizes） and mass ratio τ=~↑m/m must be satisfied τ=~↑m/m=ρ（ρ＋3）（3＋2ρ＋ρ^2）^-3/2＋ρ（-ρ＋3）（3-2ρ＋ρ^2）^-3/2-4.2^-3/2ρ^-2-^-1ρ^-2/2（1＋ρ）（3＋2ρ＋ρ^2）^-3/2＋2（ρ-1）（3-2ρ＋ρ^2）^-3/2-4（2√2）^-3ρ, and for any mass ratio τ, when mass ratio r is in the open interval （0, 0.03871633950 ... ）, there exist three central configuration solutions（the initial configuration conditions who imply hamagraphic solutions） corresponding radius ratios are r1, r2, and r3, two of them in the interval （2.639300779… , ＋∞） and one is in the interval （0.7379549890…, 1.490942703… ）. when mass ratio τ is in the open interval （130.8164950… , ＋∞）, in the same way there have three corresponding radius ratios, two of them in the interval （0, 0.4211584789... ） and one is in the interval （0.7379549890…, 1.490942703…）. When mass ratio τ is in the open interval （0.03871633950…, 130.8164950…）, there has only one solution r in the interval （0.7379549890…, 1.490942703… ）.
文摘The minimum energy and stable configurations in the spherical,equal mass full 4-body problem are investigated.This problem is defined as the dynamics of finite density spheres which interact gravitationally and through surface contact forces.This is a variation of the gravitational n-body problem in which the bodies are not allowed to come arbitrarily close to each other(due to their finite density),enabling the existence of resting configurations in addition to orbital motion.Previous work on this problem has outlined an efficient and simple way in which the stability of configurations in this problem can be defined.This methodology is applied to the 4-body problem,where we find multiple resting equilibrium configurations and outline the stability of a number of these.The study of these configurations is important for understanding the mechanics and morphological properties of small rubble pile asteroids.These results can also be generalized to other configurations of bodies that interact via field potentials and surface contact forces.
